The corotational stability postulate: Positive incremental Cauchy stress moduli for diagonal, homogeneous deformations in isotropic nonlinear elasticity Full article
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International Journal of Non-Linear Mechanics
ISSN: 0020-7462 |
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| Output data | Year: 2025, Volume: 174, Article number : 105033, Pages count : 19 DOI: 10.1016/j.ijnonlinmec.2025.105033 | ||||||
| Tags | Hill’s inequality, Drucker-stability, Second order internal work, Quasistatic loading, Constitutive stability, Material stability, Corotational stability postulate, Rate-formulation, Stress increases with strain, Positive incremental moduli, LH-ellipticity | ||||||
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Funding (1)
| 1 | Министерство науки и высшего образования Российской Федерации | FWGG-2021-0012 |
Abstract:
In isotropic nonlinear elasticity the corotational stability postulate (CSP) is the requirement that ⟨D◦D [ ], ⟩ > 0 ∀ ∈ Sym(3) ⧵ {0} , (0.1) where D◦D is any corotational stress rate, is the Cauchy stress and = sy m is the Eulerian rate of deformation tensor where = ̇ −1 = D is the spatial velocity gradient. For ̂ (log ) ∶= ( ) it is equivalent almost everywhere to the monotonicity (TSTS-M+) ⟨̂ (log 1) − ̂ (log 2), log 1 − log 2⟩ > 0 ∀ 1, 2 ∈ Sym++(3), 1 ≠ 2 . (0.2) For hyperelasticity, (CSP) is in general independent of convexity of the mapping ↦ W( ) or ↦ ̂ W( ). Considering a family of diagonal, homogeneous deformations ↦ ( ) one can, nevertheless, show that (CSP) implies positive incremental Cauchy stress moduli for this deformation family, including the incremental Young’s modulus, the incremental equibiaxial modulus, the incremental planar tension modulus and the incremental bulk modulus. Aside, (CSP) is sufficient for the Baker-Ericksen and tension-extension inequality. Moreover, it implies local invertibility of the Cauchy stress–stretch relation. Together, this shows that (CSP) is a reasonable constitutive stability postulate in nonlinear elasticity, complementing local material stability viz. LH-ellipticity.
Cite:
Neff P.
, Husemann N.J.
, Nguetcho Tchakoutio A.S.
, Korobeynikov S.N.
, Martin R.J.
The corotational stability postulate: Positive incremental Cauchy stress moduli for diagonal, homogeneous deformations in isotropic nonlinear elasticity
International Journal of Non-Linear Mechanics. 2025. V.174. 105033 :1-19. DOI: 10.1016/j.ijnonlinmec.2025.105033 WOS
The corotational stability postulate: Positive incremental Cauchy stress moduli for diagonal, homogeneous deformations in isotropic nonlinear elasticity
International Journal of Non-Linear Mechanics. 2025. V.174. 105033 :1-19. DOI: 10.1016/j.ijnonlinmec.2025.105033 WOS
Dates:
| Submitted: | Nov 21, 2024 |
| Accepted: | Jan 31, 2025 |
| Published online: | Feb 18, 2025 |
| Published print: | Mar 5, 2025 |
Identifiers:
| Web of science: | WOS:001438544500001 |
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